Question

A coordinate plane with a line drawn passing through the points (0, 3) and (1,1).
Which equation represents the graphed function?

y = –2x + 3
y = 2x + 3
y = x + 3
y = –x + 3

Answer 1

To find the equation of the line passing through the points (0, 3) and (1, 1), we first need to determine the slope of the line between these two points.

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (0, 3) and (1, 1):

- \((x_1, y_1) = (0, 3)\)
- \((x_2, y_2) = (1, 1)\)

Now, plug in the coordinates:

\[
m = \frac{1 - 3}{1 - 0} = \frac{-2}{1} = -2
\]

Now that we have the slope (\( m = -2 \)), we can use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Using the point (0, 3) for \( (x_1, y_1) \):

\[
y - 3 = -2(x - 0)
\]

Simplifying this equation:

\[
y - 3 = -2x
\]
\[
y = -2x + 3
\]

Therefore, the equation that represents the graphed function is:

\[
\boxed{y = -2x + 3}
\]